An inequality for a two variable function

In summary, an inequality is a mathematical expression that compares two quantities using symbols such as <, >, ≤, or ≥. It is different from an equation, which uses an equal sign (=) to show equality. An inequality for a two variable function is typically written in the form of f(x,y) < or > g(x,y), and its purpose is to show the relationship between two variables and determine the set of values that satisfy the inequality. To graph an inequality for a two variable function, points can be plotted on a coordinate plane and the region satisfying the inequality can be shaded.
  • #1
amirmath
8
0
Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that
##
F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big).
##
 
Physics news on Phys.org
  • #2
You'd start by considering what sort of curve is described by the part in parentheses in the second relation.
What role does c play? Is there a minimum value that the first expression can take?
 

Related to An inequality for a two variable function

1. What is an inequality?

An inequality is a mathematical expression that compares two quantities and indicates whether one is greater than, less than, or equal to the other.

2. How is an inequality different from an equation?

An inequality uses symbols such as <, >, ≤, or ≥ to compare two quantities, while an equation uses an equal sign (=) to show that two expressions are equal.

3. How is an inequality for a two variable function written?

An inequality for a two variable function is typically written in the form of f(x,y) < or > g(x,y), where f(x,y) and g(x,y) are two functions with x and y as variables.

4. What is the purpose of an inequality for a two variable function?

The purpose of an inequality for a two variable function is to show the relationship between two variables, and to determine the set of values that satisfy the inequality.

5. How do you graph an inequality for a two variable function?

To graph an inequality for a two variable function, you can plot points on a coordinate plane that satisfy the inequality and shade the region that represents the set of values that satisfy the inequality.

Similar threads

I On limit of convolution of function with a summability kernel
    • Topology and Analysis
Replies
2
Views
497
I Question about branch of logarithms
    • Topology and Analysis
Replies
14
Views
591
I In Euclidian space, closed ball is equal to closure of open ball
    • Topology and Analysis
Replies
7
Views
2K
I Regarding Wirtinger's inequality
    • Topology and Analysis
Replies
4
Views
430
A Regarding fibrations between smooth manifolds
    • Topology and Analysis
Replies
1
Views
877
I How do I separate the real and imaginary parts of an infinite product?
    • Topology and Analysis
Replies
5
Views
1K
I Showing equivalence of two definitions of essential supremum
    • Topology and Analysis
Replies
1
Views
329
MHB F is partially differentiable in (0,0) but not total differentiable
    • Topology and Analysis
Replies
11
Views
976
I Question about inverse function
    • Topology and Analysis
Replies
2
Views
1K
I Are slices of measurable functions measurable?
    • Topology and Analysis
Replies
3
Views
250

Hot Threads

Recent Insights

Back
Top